How We Measure the Distance to Stars and the Moon — Parallax and Triangulation

Parallax you can check with your finger

Stretch out your arm, hold up your thumb, and close one eye and then the other in turn. Your thumb appears to jump left and right against the distant background. This effect — where the direction of a nearby object shifts as your viewing position changes — is called "parallax." The closer your finger, the more it jumps; the farther away, the less it moves.

Astronomers use exactly this parallax to measure the distance to objects no ruler can reach. As long as you know the distance between two viewpoints (the baseline) and the angle by which the direction shifts, the geometry of a triangle lets you calculate the distance.

The distance to the Moon

The Moon is relatively close, so if two widely separated cities on Earth observe it at the same instant, its position among the stars appears to shift slightly. Knowing the distance between those two points and the shift angle θ, triangulation gives the distance to the Moon. The ancient Greek astronomer Hipparchus had already used this method to obtain the astonishingly accurate value that the Moon lies about 30 Earth-diameters away.

Today we fire lasers at the reflectors the Apollo astronauts left on the Moon's surface and measure the distance from the time the light takes to return. This has revealed that the Moon's average distance is about 384,000 km — and that it is drifting away from the Earth by about 3.8 cm every year.

The distance to the stars — annual parallax

The stars are far more distant, so two points on Earth alone reveal no shift. Astronomers therefore use the longest possible baseline — the "diameter of the Earth's orbit" around the Sun. Photograph the same star six months apart, and as the Earth moves to the opposite side of its orbit, a nearby star appears to move ever so slightly against the far background stars. Half the angle of this shift is called the "annual parallax p."

This angle is unbelievably small. Even the nearest star has an annual parallax of less than one arcsecond (1/3600 of a degree). That is why no one could measure the distance to a star until 1838, when Bessel first measured the annual parallax of the star 61 Cygni.

The unit of distance — the parsec

Annual parallax and distance are linked by a wonderfully simple relationship. When the annual parallax p is measured in "arcseconds (″)," the distance is its reciprocal, in units of "parsecs (pc)."

One step further — the cosmic ladder

Only relatively nearby stars have distances that annual parallax can measure. For more distant objects, astronomers use "standard candles" of known brightness (Cepheid variables, Type Ia supernovae), judging distance by how much their apparent brightness has dimmed. This process of joining method to method, step by step from the near to the far to measure the size of the universe, is what astronomers call the "cosmic distance ladder."